The invention is directed to improvements in devices for measuring the mass of a flowing medium using a temperature-dependent resistor in the flow path. Such a device for measuring the mass of a flowing medium in which a hot wire or hot strip is used as the temperature-dependent resistor is known in the art. The hot wire or hot strip is tautly suspended over a multiplicity of fastening points in a sensor ring. Such a device may be subjected to forces in extreme cases (impact, vibration, temperature stresses), which cause the permissible tension in the hot wire or hot strip to be exceeded. As a result, a permanent deformation of the hot wire or hot strip occurs, which unacceptably increases the resistance value of the temperature-dependent resistor.